T-Test Calculator for One-Sample, Paired, and Two-Sample Tests
Calculate a t statistic, degrees of freedom, p-value, critical value, and hypothesis-test decision. Use this t-test calculator for one-sample tests, paired samples, Welch independent samples, or pooled independent samples when equal variances are justified.
- One-sample t-test Compare a sample mean with a hypothesized population mean when the sample standard deviation is known.
- Welch two-sample t-test Compare two independent means without assuming equal variances. Welch is the safer default for most assignments.
- Pooled two-sample t-test Use the equal-variance version only when your course or analysis justifies the pooled assumption.
- Paired t-test Analyze before-after, matched-pair, or repeated-measure differences from the mean and SD of the differences.
Calculate a T-Test
Choose the design that matches your data. If your two groups are independent and the assignment does not explicitly require equal variances, use Welch's two-sample t-test.
Results
Calculator Methodology and Validation
The calculator uses the Student t cumulative distribution function and a bisection inverse CDF for critical values. Welch degrees of freedom are calculated using the Welch-Satterthwaite equation and are not rounded before computing the p-value.
| Validation case | Expected result | Purpose |
|---|---|---|
| One-sample default | t = 3.5484, df = 24, two-tailed p about 0.001634 | Checks one-sample statistic, p-value, and two-tailed critical value. |
| Welch two-sample default | t = 1.7919, df about 55.98, two-tailed p about 0.07865 | Checks fractional Welch degrees of freedom and decision logic. |
| Paired default | t = 3.0827, df = 19, two-tailed p about 0.006127 | Checks paired summary-statistic calculation. |
Common T-Test Mistakes
- Using a two-sample t-test for paired before-after data instead of a paired t-test.
- Using the pooled equal-variance option when the two sample variances are clearly different.
- Reporting only the p-value without the t statistic, degrees of freedom, alpha, and conclusion.
- Treating statistical significance as proof that the difference is practically important.
T-Test Calculator FAQs
Which t-test should I use?
Use one-sample when comparing one mean to a target value, paired when the same cases are measured twice or matched, and independent two-sample when comparing two separate groups.
Should I use Welch or pooled two-sample t-test?
Welch is usually the safer default because it does not assume equal population variances. Use pooled only when the equal-variance assumption is required and justified.
What does the t-test p-value mean?
The p-value is the probability, assuming the null hypothesis is true, of observing a t statistic at least as extreme as the one calculated.
Can this replace SPSS, R, Stata, or Excel output?
It can check the calculation, but many assignments also require software output, assumptions, effect size, and a written interpretation.
Need Help Interpreting a T-Test?
If your assignment also needs assumptions, effect size, software output, or APA reporting, share the complete prompt and data context so a statistics tutor can help you review the method.
Use Calculators Responsibly
Use this calculator to check your t-test setup, compare software output, and prepare tutoring questions. For graded work, follow your course rules and show the required method.